# 95. Unique Binary Search Trees II
## Problem Statement
Given an integer `n`, return *all the structurally unique **BST'**s (binary search trees), which has exactly* `n` *nodes of unique values from* `1` *to* `n`. Return the answer in **any order**.
**Example 1:**
Input: n = 3
Output: [[1,null,2,null,3],[1,null,3,2],[2,1,3],[3,1,null,null,2],[3,2,null,1]]
**Example 2:**
Input: n = 1
Output: [[1]]
**Constraints:**
* `1 <= n <= 8`
## Intuition
```
Building all the left subtrees in that range and attaching
Let say 1 3 , It will have all trees possilble from 1 to 3
This will be attach all the trees between 1 & 3 to left
and so on
We can use DP to memoize but no need as constraints are low
```
### Links
### Video Links
### Approach 1:
```
Recursion
```
{% code title="C++" lineNumbers="true" %}
```cpp
class Solution {
public:
vector buildTree(int start, int end) {
vector ans;
if(start > end) {
ans.push_back(NULL);
return ans;
}
for(int i = start; i <= end; ++i) {
vector leftSubTree = buildTree(start, i - 1);
vector rightSubTree = buildTree(i + 1, end);
/*
Building all the left subtrees in that range and attaching
Let say 1 3 , It will have all trees possilble from 1 to 3
This will be attach all the trees between 1 & 3 to left
and so on
*/
for(int j = 0; j < leftSubTree.size(); j++) {
for(int k = 0; k < rightSubTree.size(); k++) {
TreeNode* root = new TreeNode(i);
root->left = leftSubTree[j];
root->right = rightSubTree[k];
ans.push_back(root);
}
}
}
return ans;
}
vector generateTrees(int n) {
return buildTree(1, n);
}
};
```
{% endcode %}
### Approach 2:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Approach 3:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Approach 4:
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Similar Problems
###
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